Factorial Calculator
Visualize how factorial is calculated using iterative and recursive approaches
Factorial Visualization
Calculation Method:
Iterative
Calculating:
5! = 120
Current Step
Completed
Pending
Mathematical Definition:
n! = n × (n-1) × (n-2) × ... × 2 × 1
Special case: 0! = 1
Input Controls
Uses a loop to calculate factorial step by step
Calculation Controls
Algorithm Analysis
Time Complexity
Iterative:
O(n)
Recursive:
O(n)
Space Complexity
Iterative:
O(1)
Recursive:
O(n)
Current Statistics
Input:
5
Method:
iterative
Total Steps:
0
Current Step:
0
Result:
Calculating...
Algorithm Properties
Iterative Approach:
- • Space Efficient: Uses constant O(1) space
- • Simple: Easy to understand and implement
- • No Stack Overflow: No risk of call stack overflow
- • Predictable: Linear execution pattern
Recursive Approach:
- • Elegant: Matches mathematical definition
- • Intuitive: Natural recursive structure
- • Stack Usage: Uses O(n) call stack space
- • Risk: Can cause stack overflow for large n
How Factorial Works
Mathematical Definition: n! = n × (n-1) × (n-2) × ... × 2 × 1
Base Case: 0! = 1 and 1! = 1
Iterative: Use a loop to multiply numbers from 1 to n
Recursive: n! = n × (n-1)! with base case n ≤ 1
Performance Comparison
Iterative:
- • Time: O(n)
- • Space: O(1)
- • No stack overflow
- • More memory efficient
Recursive:
- • Time: O(n)
- • Space: O(n)
- • Risk of stack overflow
- • More elegant code
Real-World Applications
- • Combinatorics: Counting permutations and combinations
- • Probability: Calculating probabilities in statistics
- • Algorithms: Dynamic programming and recursive algorithms
- • Mathematics: Taylor series and mathematical analysis
- • Computer Science: Analysis of algorithms and complexity
Common Factorial Values
0! =1
1! =1
2! =2
3! =6
4! =24
5! =120
6! =720
7! =5,040